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Comptes Rendus Mathématique
Volume 335, n° 9
pages 745-750 (novembre 2002)
Doi : S1631-073X(02)02506-2
Received : 21 June 2002 ;  accepted : 1 July 2002
Chow-Künneth projectors for modular varieties
Projecteurs de Chow-Künneth pour des variétés modulaires
 

B.Brent Gordon a , Masaki Hanamura b , Jacob P. Murre c
a Department of Mathematics, University of Oklahoma, 601 Elm, Room 423, Norman, OK 73019, USA 
b Graduate School of Mathematics, Kyushu University, Fukuoka, 812 Japan 
c Department of Mathematics, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands 

Note presented by Christophe Soulé

Abstract

We show the existence of the Chow-Künneth projectors for certain varieties, including Kuga-Shimura varieties of Hilbert modular varieties. The Chow-Künneth projectors of a smooth projective variety are, by definition, mutually orthogonal idempotents of the Chow ring of self-correspondences which give decomposition of the total cohomology of the variety into degree pieces. To cite this article: B.B. Gordon et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 745-750.

The full text of this article is available in PDF format.
Résumé

Nous démontrons l'existence des projecteurs de Chow-Künneth pour certaines variétés, incluant les variétés de Kuga-Shimura des variétés modulaires de Hilbert. Les projecteurs de Chow-Künneth d'une variété lisse projective sont par définition des idempotents orthogonaux de l'anneau de Chow des auto-correspondances qui donnent la décomposition par les degrés de la cohomologie totale de la variété. Pour citer cet article : B.B. Gordon et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 745-750.

The full text of this article is available in PDF format.


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